Last updated :
28th July 2005
List of some Recent Publications of
Isaak A. Kunin
pertaining to his work in Nonlinear Dynamics:
( number is the
publication number from Prof. Kunin's curriculum vitae listed on his
reprints contact : kunin AT uh.edu OR ciyyunni AT uh.edu
S. Preston, I. Kunin, Yu. Gliklikh, G. Chernykh, "On the Geometrical
Aspects of Chaotic Dynamics",International
Journal of Engineering Science, v 41, 2003, pp 495-506.
176. V. Kreinovich, I. Kunin, "Kolmogorov
Complexity and chaotic Phenomena",International
Journal of Engineering Science, v 41, 2003, pp 483-493.
B. Yamrom, I. Kunin, G. Chernykh, "Method of algorithmic
transformations with applications to chaotic systems",International
Journal of Engineering Science, v 41, 2003, pp 475-482.
B. , Kunin, I.; Chernykh, G., "Centroidal Trajectories and Frames for
Chaotic Dynamical Systems", International Journal of Engineering
Science, v 41, 2003, p 465-473.
I. Hussain, F.; Zhou, X., "On multiple routes to chaos in advection
induced by point vortices", International Journal of Engineering
Science, v 41, n 3-5, March, 2003, p 459-464
Chaotic advection induced by periodic motions of point vortices
and outside of a circular domain and in the infinite plane is analyzed.
Though simple, this model flow captures multiple routes to chaos and
gives a good qualitative picture of advection in more complicated
domains such as rectangle and ellipse. Different scenarios of chaotic
advection depend on the topology of unperturbed phase portraits and
type of perturbations. In addition to the typical KAM cases, we find
scenarios accounting for inherent singularity of the velocity field. (13 refs.)
B. , Kunin, I.; Metcalfe, R.; Chernykh, G., "Discrete systems of
controlled pendulum type", International Journal of Engineering
Science, v 41, n 3-5, March,
2003, p 449-458
challenging class of controlled pendulum (CP) type systems has been
introduced in [I.A. Kunin, B. Kunin, Proc. 39th Annual Conf. Soc. Eng.
Sci., Penn State University, University Park, PA, October 2002] in
which examples have been computed using standard floating-point
methods. This work deals with recently developed discrete methods
[B.Yamrom, I.A. Kunin, G.A. Chernykh, Proc. 39th Annual Conf. Soc. Eng.
Sci., Penn State University, University Park, PA, October 2002; I.A.
Kunin, N. Shamsundar, R.W. Metcalfe, A Discrete Approach to Continuous
Chaotic Systems, in preparation] applied to the same CP type systems in
order to compare results using the two approaches and to address the
issue of extracting additional information about the system that cannot
readily be obtained using floating-point methods. These include such
features as discrete cycles and transients leading to such cycles. (8 refs.)
Kunin, B.; Chernykh, G. "Lorenz-type controlled pendulum",
International Journal of Engineering
Science, v 41, n 3-5, March, 2003, p 433-448
is known that the popular Lorenz system admits an equivalent
representation as a controlled Duffing system. It is also known that
the Duffing system is an approximation to the simple pendulum. We
introduce a new class of controlled pendulum systems that may also be
interpreted as Pendulum-Lorenz systems. These systems contain the
Lorenz system as an approximation and have a wide range of potential
applications. Examples of chaotic attractors associated with a
controlled pendulum system are presented. © 2002 Elsevier Science
All rights reserved. (11 refs.)
I., "On extracting physical information from mathematical models of
chaotic and complex systems", International Journal of
Engineering Science, v 41, n 3-5,
March, 2003, p 417-432
The paper describes a multi-structural approach to the problem
indicated in the title. In analogy with quantum mechanics, at the core
of the approach are two notions: states and (generalized) observables.
This motivates us to distinguish between mathematical and physical
dynamical systems. The first class deals with mathematical models and
states (solutions) only. The second one adds physical realizations and
observables, i.e. all methods of extracting useful information.
Observables include: renormalization, optimal gauging,
covering-coloring, discretization, tensorial measures of chaos, etc.
The corresponding algorithms are correlated to Kolmogorov complexity
and are intrinsic parts of observables, and thus of physical systems.
The approach is illustrated by examples. © 2002 Elsevier Science
All rights reserved. (27 refs.)
I. Kunin, A. Runov, "A class of Lorenz-type systems, their
factorizations and extensions, arXiv:math .DS /0105149v1, 17 May 2001.
I. , Hussain, F.; Zhou, Z.; Kovich,
D.,"Dynamics of point vortices in a special rotating frame",
International Journal of Engineering Science, v 28, n 9, 1990, p
special rotating frame (SRF) is found in which the relative motion of
point vortices is simpler, has minimum energy and reveals dynamical
features not discernible in the usual fixed frame. The angular velocity
of this frame is a solution of the equations of motion and generally is
not constant. Examples of periodic, quasiperiodic and chaotic motions
with respect to the SRF show that: (a) periodic orbits are closed lines
(not space filling as in the fixed frame, (b) quasiperiodic orbits form
steady patterns and (c) chaotic motions create asymptotic symmetries
that reflect permutation symmetry of the Hamiltonian. (8 refs.)
Kunin, I.; Gliklikh, Y.E.; Chernykh, G.,"On the geometrical
characteristics of chaotic dynamics, I", International Journal
of Engineering Science, v 41, n 3-5, March, 2003, p 495-506
The geometrical characteristics of chaotic dynamics were presented. It
was found that these structures carry important information about the
properties of dynamical system: all curvatures of trajectories,
Lyapunov exponents etc. The numerical calculations of curvatures of
eigenvalues of these tensors along trajectories of Lorentz system
displayed sharp change of behavior near the points where trajectories
leave the fractal surface of attractor. (12 refs.) (Edited
141. Kunin, I., "Duffing Lorenz type
systems", International Conference in honor of V. Arnold, 1997, The Fields Institute, Toronto, Canada.
I.; Prishepionok, S.,"G-moving frames and their applications in
dynamics", International Journal of Engineering
Science, v 33, n 15, Dec, 1995, Edelen Symposium, p
Conference: Proceedings of the 31st
Annual Technical Meeting of the Society of Engineering Science, Oct
10-12 1994, College Station, TX, USA